Let's connect the equation of a line, with the graph and the data.
Use the sliders (or input your numbers into the boxes). Several thing change in the applet when you make changes.
What changes in the graph when you change the slope? The y-intercept?
What changes in the table? Do the values change the same way?
Let's dig a little deeper in the data.
What does =(B17-B16)/(A17-A16) calculate? Enter this formula in C17 to find out. Drag this formula down to fill in through the last input line. What do you notice? This formula used on a set of data is often called "1st differences"? Why is is called this?
Change the slope and y-intercept sliders again. What do you notice about the 1st differences?
Based on your observations what do you think is true about 1st differences for linear equations? Will this be true for any equation? How could you check? Design what you could do.